cornwell,group theory in physics--an introduction

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1、GroupTheoryinPhysicsAnIntroductionJ.F.CornwellSchoolofPhysicsandAstronomyUniversityofSt.Andrews,ScotlandACADEMICPRESSHarcourtBrace&Company,PublishersSanDiegoLondonBostonNewYorkSydneyTokyoTorontoThisbookisprintedonacid-freepaperAcademicPress525BStreet,Suite1900,SanDiego,

2、California92101-4495,USAhttp://www.apnet.comAcademicPressLimited24-28OvalRoad,LondonNWl7DX,UKhttp://~wcw,hbuk.co.uk/ap/Copyright(~)1997byACADEMICPRESSAllrightsreservedNopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeanselectronicormechanical,includin

3、gphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher.AcataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloguing-in-PublicationDataISBN0-12-189800-8PrintedandboundbyAntonyRoweLtd,Eastboume9

4、79899000102EB987654321ContentsPrefaceviiTheBasicFramework11Theconceptofagroup.......................12Groupsofcoordinatetransformations..............4(a)Rotations..........................5(b)Translations.........................9ThegroupoftheSchr5dingerequation........

5、......10(a)TheHamiltonianoperator.................10(b)TheinvarianceoftheHamiltonianoperator.......11(c)ThescalartransformationoperatorsP(T)........12Theroleofmatrixrepresentations................15TheStructureofGroups191Someelementaryconsiderations..................192

6、Classes................................213Invariantsubgroups........................234Cosets................................245Factorgroups............................266Homomorphicandisomorphicmappings.............287Directproductsandsemi-directproductsofgroups.......

7、31LieGroups351DefinitionofalinearLiegroup..................352TheconnectedcomponentsofalinearLiegroup........403TheconceptofcompactnessforlinearLiegroups........424Invariantintegration........................44RepresentationsofGroups-PrincipalIdeas471Definitions........

8、......................472Equivalentrepresentations.....................493Unitaryrepresentations..............